## Slice sampling with adaptive
multivariate steps: The shrinking-rank method

**Madeleine Thompson,
Dept. of Statistics, University of Toronto**

**Radford M. Neal,
Dept. of Statistics and Dept. of Computer Science, University of Toronto
**
The shrinking rank method is a variation of slice sampling that is
efficient at sampling from mul- tivariate distributions with highly
correlated parameters. It requires that the gradient of the log-
density be computable. At each individual step, it approximates the
current slice with a Gaussian occupying a shrinking-dimension
subspace. The dimension of the approximation is shrunk orthogo- nally
to the gradient at rejected proposals, since the gradients at points
outside the current slice tend to point towards the slice. This causes
the proposal distribution to converge rapidly to an estimate of the
longest axis of the slice, resulting in states that are less
correlated than those generated by related methods. After describing
the method, we compare it to two other methods on several
distributions and obtain favorable results.

*JSM 2010, Section on Statistical Computing*, pp. 3890-3896:: pdf.

**Associated references:**
The following technical report is related to the conference paper above:
Thompson, M. and Neal, R. M. (2010) ``Covariance-adaptive slice sampling'',
Technical Report No. 1002, Dept. of Statistics, University of Toronto,
17 pages:
abstract,
postscript,
pdf.